This protocol tests the hypothesis that subjects who have failed antiretroviral treatment regimens containing one or more protease inhibitors will experience a virologic response to a regimen utilizing combinations of currently approved protease inhibitors and the investigational agents amprenavir (a protease inhibitor), abacavir (a nucleoside reverse transcriptase inhibitor [NRTI]), adefovir dipivoxil (a nucleotide RTI), and efavirenz (a non-nucleoside RTI), and will tolerate these multidrug regimens. Recent advances in antiretroviral therapy have altered dramatically the prognosis of HIV-infected individuals. Although treatment regimens that include a protease inhibitor provide durable suppression of HIV-1 replication in a substantial number of patients, treatment failure due to emergence of drug-resistant virus is a growing problem. No single drug or drug regimen has demonstrated potency in patients who have failed one or more protease inhibitor-containing regimens. Drug resistance testing might provide some guidance in this setting but assays are neither widely available nor clinically validated. This study is to determine how may people will have an undetectable amount of HIV in their blood by week 24 and if the new drugs are tolerated, taken in combination with drugs which are already FDA approved. The newer drugs have been tested in a small number of volunteers and have shown that they may be helpful in preventing HIV from multiplying in the body. Study participants will be assigned to one of four groups to receive study drugs partially based on protease inhibitors they have taken in the past and partially based on chance randomization. The amount of HIV in the participant's blood will be measured at regular intervals to determine drug effectiveness.